{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4UOQL4FMGSB7Q7VNJEEIMJ7Z3X","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"45e6ea1e9d580fd1bafc7416b631722025dd099208701a0b42a043000c66598f","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-04T22:00:37Z","title_canon_sha256":"27dfd7866698adcf67d19b7e24cd98b7fa008f2f83971b7c359c2a8e5a3c7aee"},"schema_version":"1.0","source":{"id":"1511.01528","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.01528","created_at":"2026-05-18T01:03:10Z"},{"alias_kind":"arxiv_version","alias_value":"1511.01528v2","created_at":"2026-05-18T01:03:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01528","created_at":"2026-05-18T01:03:10Z"},{"alias_kind":"pith_short_12","alias_value":"4UOQL4FMGSB7","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4UOQL4FMGSB7Q7VN","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4UOQL4FM","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:145fb97d954c485c726a36b9ecf2db9441b7c9f6e0e55078743d4ae7730f9f9a","target":"graph","created_at":"2026-05-18T01:03:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study pointwise convergence of entangled averages of the form \\[ \\frac{1}{N^k}\\sum_{1\\leq n_1,\\ldots, n_k\\leq N} T_m^{n_{\\alpha(m)}}A_{m-1}T^{n_{\\alpha(m-1)}}_{m-1}\\ldots A_2T_2^{n_{\\alpha(2)}}A_1T_1^{n_{\\alpha(1)}} f, \\] where $f\\in L^2(X,\\mu)$, $\\alpha:\\left\\{1,\\ldots,m\\right\\}\\to\\left\\{1,\\ldots,k\\right\\}$, and the $T_i$ are ergodic measure preserving transformations on the standard probability space $(X,\\mu)$. We show that under some joint boundedness and twisted compactness conditions on the pairs $(A_i,T_i)$, almost everywhere convergence holds for all $f\\in L^2$. We also present resul","authors_text":"D\\'avid Kunszenti-Kov\\'acs","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-04T22:00:37Z","title":"Almost everywhere convergence of entangled ergodic averages"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01528","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:71f9ec80f0eae1a0bbb0be4572d168ee813b0fbf785dda8f9e0a65a96854413e","target":"record","created_at":"2026-05-18T01:03:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"45e6ea1e9d580fd1bafc7416b631722025dd099208701a0b42a043000c66598f","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-04T22:00:37Z","title_canon_sha256":"27dfd7866698adcf67d19b7e24cd98b7fa008f2f83971b7c359c2a8e5a3c7aee"},"schema_version":"1.0","source":{"id":"1511.01528","kind":"arxiv","version":2}},"canonical_sha256":"e51d05f0ac3483f87ead49088627f9ddd971707a74948e8ad42a0f893947b9aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e51d05f0ac3483f87ead49088627f9ddd971707a74948e8ad42a0f893947b9aa","first_computed_at":"2026-05-18T01:03:10.760522Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:10.760522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KjjdG+dBC6hUNExnLJZIoXInQAgtvFp/hUFzgMnqfrbm7m/sMKfFxT3SJvfXxLagN1bWkNQDs7XovMWrsORvDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:10.761129Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.01528","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71f9ec80f0eae1a0bbb0be4572d168ee813b0fbf785dda8f9e0a65a96854413e","sha256:145fb97d954c485c726a36b9ecf2db9441b7c9f6e0e55078743d4ae7730f9f9a"],"state_sha256":"8c6b4600ba8d9ebdb4b5ff292ca0cf47035e5e764f4a45b3a6799361f60b9f0b"}